Question: Given $ m \angle LOM = 3x + 22$, and $ m \angle MON = 4x + 123$, find $m\angle MON$. $O$ $L$ $N$ $M$
From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 22} + {4x + 123} = {180}$ Combine like terms: $ 7x + 145 = 180$ Subtract $145$ from both sides: $ 7x = 35$ Divide both sides by $7$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 4({5}) + 123$ Simplify: $ {m\angle MON = 20 + 123}$ So ${m\angle MON = 143}$.